Research Article
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Year 2020, , 90 - 95, 20.09.2020
https://doi.org/10.26701/ems.669495

Abstract

References

  • Eringen, A.C., (1972). Nonlocal polar elastic continua. International Journal of Engineering Science, Doi: 10.1016/0020-7225(72)90070-5.
  • Eringen, A.C., (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics 54(9): 4703–10, Doi: 10.1063/1.332803.
  • Peddieson, J., Buchanan, G.R., McNitt, R.P., (2003). Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science 41(3–5): 305–12, Doi: 10.1016/S0020-7225(02)00210-0.
  • Wang, L., Hu, H., (2005). Flexural wave propagation in single-walled carbon nanotubes. Phys. Rev. B 71(19): 195412, Doi: 10.1103/PhysRevB.71.195412.
  • Wang, Q., (2005). Wave propagation in carbon nanotubes via nonlocal continuum mechanics. Journal of Applied Physics 98(12): 124301, Doi: 10.1063/1.2141648.
  • Wang, Q., Varadan, V.K., (2006). Wave characteristics of carbon nanotubes. International Journal of Solids and Structures 43(2): 254–65, Doi: 10.1016/j.ijsolstr.2005.02.047.
  • Reddy, J.N.N., (2007). Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science 45(2–8): 288–307, Doi: 10.1016/j.ijengsci.2007.04.004.
  • Wang, Q., Wang, C.M., (2007). The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology 18(7): 075702, Doi: 10.1088/0957-4484/18/7/075702.
  • Aydogdu, M., (2009). A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration. Physica E: Low-Dimensional Systems and Nanostructures 41(9): 1651–5, Doi: 10.1016/j.physe.2009.05.014.
  • Ansari, R., Ajori, S., (2015). A molecular dynamics study on the vibration of carbon and boron nitride double-walled hybrid nanotubes. Applied Physics A: Materials Science and Processing 120(4): 1399–406, Doi: 10.1007/s00339-015-9324-8.
  • Numanoğlu, H.M., Akgöz, B., Civalek, Ö., (2018). On dynamic analysis of nanorods. International Journal of Engineering Science 130: 33–50, Doi: 10.1016/j.ijengsci.2018.05.001.
  • Demir, Ç., Civalek, Ö., (2017). On the analysis of microbeams. International Journal of Engineering Science 121: 14–33, Doi: 10.1016/j.ijengsci.2017.08.016.
  • Avcar, M., Hazim AlSaid Alwan, H., (2017). Free Vibration of Functionally Graded Rayleigh Beam. International Journal Of Engineering & Applied Sciences 9(2): 127–127, Doi: 10.24107/ijeas.322884.
  • Chang, W.-J., Lee, H.-L., (2012). Vibration analysis of viscoelastic carbon nanotubes. Micro & Nano Letters 7(12): 1308–12, Doi: 10.1049/mnl.2012.0612.
  • Lei, Y., Adhikari, S., Friswell, M.I., (2013). Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams. International Journal of Engineering Science 66–67: 1–13, Doi: 10.1016/j.ijengsci.2013.02.004.
  • Avcar, M., (2016). Pasternak Zemine Oturan Eksenel Yüke Maruz Homojen Olmayan Kirişin Serbest Titreşimi. Journal of Polytechnic 19(November): 507–12, Doi: 10.2339/2016.19.4.
  • Karličić, D., Murmu, T., Cajić, M., Kozić, P., Adhikari, S., (2014). Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field. Journal of Applied Physics 115(23): 234303, Doi: 10.1063/1.4883194.
  • Ghorbanpour Arani, A., Yousefi, M., Amir, S., Dashti, P., Chehreh, A.B., (2015). Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field. Arabian Journal for Science and Engineering 40(6): 1707–26, Doi: 10.1007/s13369-015-1650-9.
  • Farokhi, H., Ghayesh, M.H., (2017). Viscoelasticity effects on resonant response of a shear deformable extensible microbeam. Nonlinear Dynamics 87(1): 391–406, Doi: 10.1007/s11071-016-3050-4.
  • Cajic, M., Karlicic, D., Lazarevic, M., (2015). Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle. Theoretical and Applied Mechanics 42(3): 167–90, Doi: 10.2298/TAM1503167C.
  • Ansari, R., Faraji Oskouie, M., Sadeghi, F., Bazdid-Vahdati, M., (2015). Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory. Physica E: Low-Dimensional Systems and Nanostructures 74: 318–27, Doi: 10.1016/j.physe.2015.07.013.
  • Zhang, D.P., Lei, Y.J., Wang, C.Y., Shen, Z. Bin., (2017). Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation. Journal of Mechanical Science and Technology 31(1): 87–98, Doi: 10.1007/s12206-016-1007-7.
  • Zhen, Y., Zhou, L., (2017). Wave propagation in fluid-conveying viscoelastic carbon nanotubes under longitudinal magnetic field with thermal and surface effect via nonlocal strain gradient theory. Modern Physics Letters B 31(8), Doi: 10.1142/S0217984917500695.
  • Attia, M.A., Mahmoud, F.F., (2017). Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects. International Journal of Mechanics and Materials in Design 13(3): 385–406, Doi: 10.1007/s10999-016-9343-4.
  • Cajić, M., Karličić, D., Lazarević, M., (2017). Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters. Meccanica 52(1–2): 363–82, Doi: 10.1007/s11012-016-0417-z.
  • Wang, J., Shen, H., (2019). Nonlinear vibrations of axially moving simply supported viscoelastic nanobeams based on nonlocal strain gradient theory. Journal of Physics Condensed Matter 31(48), Doi: 10.1088/1361-648X/ab3bf7.
  • Naghinejad, M., Ovesy, H.R., (2019). Viscoelastic free vibration behavior of nano-scaled beams via finite element nonlocal integral elasticity approach. Journal of Vibration and Control 25(2): 445–59, Doi: 10.1177/1077546318783556.
  • Martin, O., (2019). Nonlocal effects on the dynamic analysis of a viscoelastic nanobeam using a fractional Zener model. Applied Mathematical Modelling 73: 637–50, Doi: 10.1016/j.apm.2019.04.029.
  • Pavlović, I.R., Pavlović, R., Janevski, G., (2019). Mathematical modeling and stochastic stability analysis of viscoelastic nanobeams using higher-order nonlocal strain gradient theory. Archives of Mechanics 71(2): 137–53, Doi: 10.24423/aom.3139.
  • Farajpour, A., Ghayesh, M.H., Farokhi, H., (2019). Nonlocal nonlinear mechanics of imperfect carbon nanotubes. International Journal of Engineering Science 142: 201–15, Doi: 10.1016/j.ijengsci.2019.03.003.
  • Ansari, R., Gholami, R., Ajori, S., (2013). Torsional vibration analysis of carbon nanotubes based on the strain gradient theory and molecular dynamic simulations. Journal of Vibration and Acoustics, Transactions of the ASME 135(5): 1–6, Doi: 10.1115/1.4024208.
  • Mustapha, K.B., Wong, B.T., (2016). Torsional frequency analyses of microtubules with end attachments. ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik 96(7): 824–42, Doi: 10.1002/zamm.201500007.
  • Arda, M., Aydogdu, M., (2014). Torsional statics and dynamics of nanotubes embedded in an elastic medium. Composite Structures 114(1): 80–91, Doi: 10.1016/j.compstruct.2014.03.053.
  • Flügge, W., (1975). Viscoelasticity. Berlin, Heidelberg: Springer Berlin Heidelberg.

Torsional Vibration Analysis of Carbon Nanotubes Using Maxwell and Kelvin-Voigt Type Viscoelastic Material Models

Year 2020, , 90 - 95, 20.09.2020
https://doi.org/10.26701/ems.669495

Abstract

Torsional dynamic analysis of viscoelastic Carbon Nanotubes (CNT) has been carried out in the present work. Maxwell and Kelvin-Voigt type viscoelasticity are considered in the modeling of viscoelastic material. Nonlocal Elasticity Theory is used in the formulation of governing equation of motion and boundary conditions. Viscoelasticity and nonlocal effects of structure on the free torsional vibration of CNTs have been investigated. Clamped-clamped and clamped-free boundary conditions are considered. Present study results could be useful in design of nano-medicine delivery applications.

References

  • Eringen, A.C., (1972). Nonlocal polar elastic continua. International Journal of Engineering Science, Doi: 10.1016/0020-7225(72)90070-5.
  • Eringen, A.C., (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics 54(9): 4703–10, Doi: 10.1063/1.332803.
  • Peddieson, J., Buchanan, G.R., McNitt, R.P., (2003). Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science 41(3–5): 305–12, Doi: 10.1016/S0020-7225(02)00210-0.
  • Wang, L., Hu, H., (2005). Flexural wave propagation in single-walled carbon nanotubes. Phys. Rev. B 71(19): 195412, Doi: 10.1103/PhysRevB.71.195412.
  • Wang, Q., (2005). Wave propagation in carbon nanotubes via nonlocal continuum mechanics. Journal of Applied Physics 98(12): 124301, Doi: 10.1063/1.2141648.
  • Wang, Q., Varadan, V.K., (2006). Wave characteristics of carbon nanotubes. International Journal of Solids and Structures 43(2): 254–65, Doi: 10.1016/j.ijsolstr.2005.02.047.
  • Reddy, J.N.N., (2007). Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science 45(2–8): 288–307, Doi: 10.1016/j.ijengsci.2007.04.004.
  • Wang, Q., Wang, C.M., (2007). The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology 18(7): 075702, Doi: 10.1088/0957-4484/18/7/075702.
  • Aydogdu, M., (2009). A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration. Physica E: Low-Dimensional Systems and Nanostructures 41(9): 1651–5, Doi: 10.1016/j.physe.2009.05.014.
  • Ansari, R., Ajori, S., (2015). A molecular dynamics study on the vibration of carbon and boron nitride double-walled hybrid nanotubes. Applied Physics A: Materials Science and Processing 120(4): 1399–406, Doi: 10.1007/s00339-015-9324-8.
  • Numanoğlu, H.M., Akgöz, B., Civalek, Ö., (2018). On dynamic analysis of nanorods. International Journal of Engineering Science 130: 33–50, Doi: 10.1016/j.ijengsci.2018.05.001.
  • Demir, Ç., Civalek, Ö., (2017). On the analysis of microbeams. International Journal of Engineering Science 121: 14–33, Doi: 10.1016/j.ijengsci.2017.08.016.
  • Avcar, M., Hazim AlSaid Alwan, H., (2017). Free Vibration of Functionally Graded Rayleigh Beam. International Journal Of Engineering & Applied Sciences 9(2): 127–127, Doi: 10.24107/ijeas.322884.
  • Chang, W.-J., Lee, H.-L., (2012). Vibration analysis of viscoelastic carbon nanotubes. Micro & Nano Letters 7(12): 1308–12, Doi: 10.1049/mnl.2012.0612.
  • Lei, Y., Adhikari, S., Friswell, M.I., (2013). Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams. International Journal of Engineering Science 66–67: 1–13, Doi: 10.1016/j.ijengsci.2013.02.004.
  • Avcar, M., (2016). Pasternak Zemine Oturan Eksenel Yüke Maruz Homojen Olmayan Kirişin Serbest Titreşimi. Journal of Polytechnic 19(November): 507–12, Doi: 10.2339/2016.19.4.
  • Karličić, D., Murmu, T., Cajić, M., Kozić, P., Adhikari, S., (2014). Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field. Journal of Applied Physics 115(23): 234303, Doi: 10.1063/1.4883194.
  • Ghorbanpour Arani, A., Yousefi, M., Amir, S., Dashti, P., Chehreh, A.B., (2015). Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field. Arabian Journal for Science and Engineering 40(6): 1707–26, Doi: 10.1007/s13369-015-1650-9.
  • Farokhi, H., Ghayesh, M.H., (2017). Viscoelasticity effects on resonant response of a shear deformable extensible microbeam. Nonlinear Dynamics 87(1): 391–406, Doi: 10.1007/s11071-016-3050-4.
  • Cajic, M., Karlicic, D., Lazarevic, M., (2015). Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle. Theoretical and Applied Mechanics 42(3): 167–90, Doi: 10.2298/TAM1503167C.
  • Ansari, R., Faraji Oskouie, M., Sadeghi, F., Bazdid-Vahdati, M., (2015). Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory. Physica E: Low-Dimensional Systems and Nanostructures 74: 318–27, Doi: 10.1016/j.physe.2015.07.013.
  • Zhang, D.P., Lei, Y.J., Wang, C.Y., Shen, Z. Bin., (2017). Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation. Journal of Mechanical Science and Technology 31(1): 87–98, Doi: 10.1007/s12206-016-1007-7.
  • Zhen, Y., Zhou, L., (2017). Wave propagation in fluid-conveying viscoelastic carbon nanotubes under longitudinal magnetic field with thermal and surface effect via nonlocal strain gradient theory. Modern Physics Letters B 31(8), Doi: 10.1142/S0217984917500695.
  • Attia, M.A., Mahmoud, F.F., (2017). Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects. International Journal of Mechanics and Materials in Design 13(3): 385–406, Doi: 10.1007/s10999-016-9343-4.
  • Cajić, M., Karličić, D., Lazarević, M., (2017). Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters. Meccanica 52(1–2): 363–82, Doi: 10.1007/s11012-016-0417-z.
  • Wang, J., Shen, H., (2019). Nonlinear vibrations of axially moving simply supported viscoelastic nanobeams based on nonlocal strain gradient theory. Journal of Physics Condensed Matter 31(48), Doi: 10.1088/1361-648X/ab3bf7.
  • Naghinejad, M., Ovesy, H.R., (2019). Viscoelastic free vibration behavior of nano-scaled beams via finite element nonlocal integral elasticity approach. Journal of Vibration and Control 25(2): 445–59, Doi: 10.1177/1077546318783556.
  • Martin, O., (2019). Nonlocal effects on the dynamic analysis of a viscoelastic nanobeam using a fractional Zener model. Applied Mathematical Modelling 73: 637–50, Doi: 10.1016/j.apm.2019.04.029.
  • Pavlović, I.R., Pavlović, R., Janevski, G., (2019). Mathematical modeling and stochastic stability analysis of viscoelastic nanobeams using higher-order nonlocal strain gradient theory. Archives of Mechanics 71(2): 137–53, Doi: 10.24423/aom.3139.
  • Farajpour, A., Ghayesh, M.H., Farokhi, H., (2019). Nonlocal nonlinear mechanics of imperfect carbon nanotubes. International Journal of Engineering Science 142: 201–15, Doi: 10.1016/j.ijengsci.2019.03.003.
  • Ansari, R., Gholami, R., Ajori, S., (2013). Torsional vibration analysis of carbon nanotubes based on the strain gradient theory and molecular dynamic simulations. Journal of Vibration and Acoustics, Transactions of the ASME 135(5): 1–6, Doi: 10.1115/1.4024208.
  • Mustapha, K.B., Wong, B.T., (2016). Torsional frequency analyses of microtubules with end attachments. ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik 96(7): 824–42, Doi: 10.1002/zamm.201500007.
  • Arda, M., Aydogdu, M., (2014). Torsional statics and dynamics of nanotubes embedded in an elastic medium. Composite Structures 114(1): 80–91, Doi: 10.1016/j.compstruct.2014.03.053.
  • Flügge, W., (1975). Viscoelasticity. Berlin, Heidelberg: Springer Berlin Heidelberg.
There are 34 citations in total.

Details

Primary Language English
Subjects Mechanical Engineering
Journal Section Research Article
Authors

Mustafa Arda 0000-0002-0314-3950

Publication Date September 20, 2020
Acceptance Date April 8, 2020
Published in Issue Year 2020

Cite

APA Arda, M. (2020). Torsional Vibration Analysis of Carbon Nanotubes Using Maxwell and Kelvin-Voigt Type Viscoelastic Material Models. European Mechanical Science, 4(3), 90-95. https://doi.org/10.26701/ems.669495

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